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Design of vector autoregressive processes for invariant statistics

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  • Paruolo Paolo

    (Department of Economics, University of Insubria, Italy)

Abstract

This paper discusses the Monte Carlo (MC) design of Gaussian Vector Au- toregressive processes (VAR) for the evalutation of invariant statistics. We focus on the case of cointegrated (CI) I(1) processes, linear and invertible trans- formations and CI rank likelihood ratio (LR) tests. It is found that all VAR of order 1 can be reduced to a system of independent or recursive subsystems, of computational dimension at most equal to 2. The results are applied to the indexing of the distribution of LR test statistics for CI rank under local alternatives. They are also extended to the case of VAR processes of higher order.

Suggested Citation

  • Paruolo Paolo, 2005. "Design of vector autoregressive processes for invariant statistics," Economics and Quantitative Methods qf0504, Department of Economics, University of Insubria.
    • Handle: RePEc:ins:quaeco:qf0504
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    File URL: https://www.eco.uninsubria.it/RePEc/pdf/QF2005_6.pdf
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    References listed on IDEAS

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    1. Saikkonen, Pentti & Lütkepohl, Helmut, 2000. "Testing For The Cointegrating Rank Of A Var Process With An Intercept," Econometric Theory, Cambridge University Press, vol. 16(3), pages 373-406, June.
    2. Peter Reinhard Hansen, 2005. "Granger's representation theorem: A closed-form expression for I(1) processes," Econometrics Journal, Royal Economic Society, vol. 8(1), pages 23-38, March.
    3. Lutkepohl, Helmut & Saikkonen, Pentti, 2000. "Testing for the cointegrating rank of a VAR process with a time trend," Journal of Econometrics, Elsevier, vol. 95(1), pages 177-198, March.
    4. Helmut Lütkepohl & Pentti Saikkonen & Carsten Trenkler, 2001. "Maximum eigenvalue versus trace tests for the cointegrating rank of a VAR process," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-8.
    5. Toda, Hiro Y, 1994. "Finite Sample Properties of Likelihood Ratio Tests for Cointegrating Ranks when Linear Trends are Present," The Review of Economics and Statistics, MIT Press, vol. 76(1), pages 66-79, February.
    6. Bent Nielsen, 2004. "On the Distribution of Likelihood Ratio Test Statistics for Cointegration Rank," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 1-23.
    7. Dietmar Bauer & Martin Wagner, 2002. "A Canonical Form for Unit Root Processes in the State Space Framework," Diskussionsschriften dp0204, Universitaet Bern, Departement Volkswirtschaft.
    8. Gonzalo, Jesus, 1994. "Five alternative methods of estimating long-run equilibrium relationships," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 203-233.
    9. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
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    Cited by:

    1. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 269-271, May.
    2. Jurgen A. Doornik & Rocco Mosconi & Paolo Paruolo, 2017. "Formula I(1) and I(2): Race Tracks for Likelihood Maximization Algorithms of I(1) and I(2) Cointegrated VAR Models," Econometrics, MDPI, vol. 5(4), pages 1-30, November.

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    Keywords

    Invariance; Vector autoregressive process; Monte Carlo; Likeli-hood ratio test; Cointegration.;
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